Calculus III Honors
2022 - 2023
Teacher: Mr. Cam Wieczorek
Voice mail: (847) 327-7560
E-mail: cameron.wieczorek@d128.org
Course Description: This course is a continuation of topics covered in Calculus I and Calculus II. Topics
include vectors in two and three dimensions, vector operations, lines and planes in space, vector
functions, functions of more than one variable, partial derivatives, directional derivatives, gradients, and
multiple integrals. Solid analytic geometry topics include quadric surfaces, cylindrical and spherical
coordinates and curves in 3-space. Vector calculus topics include vector fields, line integrals, surface
integrals, curl and divergence, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. This
course is a dual credit course through the College of Lake County.
Course Competencies/Objectives:
Upon completion of this course, a student should be able to:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Use vectors in applications and perform the associated operations on vectors.
Write equations of lines and planes in space.
Use cylindrical and spherical coordinate systems.
Apply the concepts of calculus to vector-valued functions and use such functions in
applications.
Demonstrate the understanding of concepts of limits and continuity in functions of several
variables.
Produce partial derivatives and differentials of functions of several variables.
Find tangent planes and normal lines.
Find extrema of functions of two variables.
Use Lagrange Multipliers to find extrema.
Find multiple integrals and use them in applications.
Use change of variables in multiple integrals.
Demonstrate an understanding of vector fields.
Find line integrals.
Apply the Fundamental Theorem of Line Integrals.
Prove a vector field is conservative by finding a potential function.
Use Green's Theorem.
Justify Green’s Theorem in the case where the underlying region is simple.
Find curl and divergence.
Find parametric representations of quadric surfaces.
Find tangent planes to points on parametric surfaces.
Find areas of parametric surfaces.
Define oriented surface.
Find surface integrals.
Use Stokes’ Theorem.
Use the Divergence Theorem.
Textbook: Stewart, James, Calculus-Early Transcendentals, 9th Edition, Cengage, 2020.
Daily Materials:
●
●
●
●
●
WebAssign access (class code will be provided on Google Classroom)
Google Classroom (main source of communication)
Chromebook and stylus – make sure Chromebook is charged!
Pencils , Highlighters, Binder/Folder, Notebook
TI-84 Calculator – make sure it is charged!
Daily Expectations:
1.
2.
3.
4.
5.
6.
7.
8.
Have your required class materials with you.
If there is a warm-up on the board, start it as soon as you walk in.
Be in your seat when the bell rings.
Be ready to learn with a positive attitude.
Ask questions and advocate for yourself.
Actively listen when someone is sharing an idea.
Use technology appropriately.
Check Google Classroom every night for important announcements and to review information
from class that day.
Evaluation and Grading:
Your grade will be based on points accumulated throughout the course:
1) Homework and Projects (20% of grade) – Homework will be assigned daily. Most of your
homework will be completed using our WebAssign software. You may also be assigned a
worksheet or online activity for homework. Homework assignments will be due on the date
specified on Google Classroom – assignments will typically have a grace period to allow you the
opportunity to ask questions about problems you are struggling with. Late homework
assignments will NOT be accepted. Occasional take-home projects or explorations may be
given to apply the calculus concepts we are learning throughout the course. Keeping up with
the homework is essential for success on the quizzes and exams in this course!
2) Exams and Quizzes (60% of grade) – 4-5 in-class exams will be given each semester covering
material from a chapter or set of related chapters; additionally, in-class quizzes covering specific
topics from a chapter will be given in preparation for the exams. Retakes will not be offered for
exams and quizzes. No test aids are allowed on exams and quizzes.
3) Final Exam (20% of grade) - A comprehensive final exam will be given at the end of the course
covering all content from both the first and second semesters. Students must take the final
exam in order to pass the course.
Grade Recovery Opportunities:
No extra credit opportunities will be provided in this course, nor should students expect exam scores to
be curved. The following opportunities are available, though, to allow you to demonstrate growth
throughout each semester:
 Exam Replacement: If a student earns a C or better on the final exam, that score will be used to
replace that student’s lowest exam grade from the semester (provided that the grade to be
replaced is lower than the grade earned on the final exam).
 Quiz Scoring: In addition, a student’s lowest three quiz scores from the course will be dropped.
COURSE OUTLINE:
CHAPTER
TOPIC
HOURS
12
Vectors and the Geometry of Space
Three-Dimensional Coordinate Systems; Vectors; The Dot Product;
The Cross Product; Equations of Lines and Plane;
Cylinders and Quadric Surfaces
13
Vector Functions
Vector Functions and Space Curves;
Derivatives and Integrals of Vector Functions; Arc Length and Curvature;
Motion in Space: Velocity and Acceleration
9
14
Partial Derivatives
Functions of Several Variables; Limits and Continuity; Partial Derivatives;
Tangent Planes and Linear Approximations; The Chain Rule;
Directional Derivatives and the Gradient Vector;
Maximum and Minimum Values; Lagrange Multipliers
21
15
Multiple Integrals
Double Integrals over Rectangles;
Double Integrals over General Regions;
Double Integrals in Polar Coordinates
Applications of Double Integrals; Surface Area;
Triple Integrals; Triple Integrals in Cylindrical Coordinates;
Triple Integrals in Spherical Coordinates;
Change of Variables in Multiple Integrals
23
16
Vector Calculus
Vector Fields; Line Integrals; The Fundamental Theorem for Line Integrals;
Green’s Theorem; Curl and Divergence; Parametric Surfaces and Their Areas;
Surface Integrals; Stokes’ Theorem; The Divergence Theorem
30
Testing and Leeway
TOTAL HOURS
15
15
113